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Studies in the History of Philosophy

On some concepts constituting discussive logic
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On some concepts constituting discussive logic

Authors

  • Marek Nasieniewski Nicolaus Copernicus University in Toruń https://orcid.org/0000-0002-9612-3990
  • Ricardo Arturo Nicolas Francisco Nicolaus Copernicus University in Toruń https://orcid.org/0000-0001-5490-9357

DOI:

https://doi.org/10.12775/szhf.2025.030

Keywords

Jaśkowski, discussive logic, S5, M-counterpart, M-fragment, translations of discussive connectives

Author Biography

Marek Nasieniewski, Nicolaus Copernicus University in Toruń

Department of Logic

References

Achtelik Gra˙ zyna, Lech Dubikajtis, El˙ zbieta Dudek, Jan Konior. 1981. “On independence of axioms in Ja´skowski discussive propositional calculus”. Reports on Mathematical Logic 11: 3–11.

Akama Seiki, Jair Minoro Abe, Kazumi Nakamatsu. 2011. “Constructive Discursive Logic with Strong Negation”. Logique et Analyse 54: 395–408.

Béziau Jean-Yves. 2006. “The paraconsistent logic Z. A possible solution to Ja´skowski’s problem”. Logic and Logical Philosophy 15: 99–111. https://doi.org/10.12775/LLP.2006.006

Błaszczuk Jerzy J., Wiesław Dziobiak. 1975b. “Modal systems related to 4 of Soboci´nski”. Bulletin of the Section of Logic 3(4): 103–106.

Błaszczuk Jerzy J., Wiesław Dziobiak. 1975a. “Modal systems placed in the “triangle" S4–T*-T''". Bulletin of the Section of Logic 3(4): 138–141.

Błaszczuk Jerzy J., Wiesław Dziobiak. 1975c. “Remarks on Perzanowski’s modal system”. Bulletin of the Section of Logic 4(2): 57–64.

Błaszczuk Jerzy J., Wiesław Dziobiak. 1976 . “An axiomatization of M-counterparts for some modal logics”. Reports on Mathematical Logic 6: 3–6

Błaszczuk Jerzy J., Wiesław Dziobiak. 1977. “Modal logics connected with systems 4 of Soboci´nski”. Studia Logica 36: 151–164. https://doi.org/10.1007/BF02121260

Ciuciura Janusz. 2006. “A quasi-discursive system ND”. Notre Dame Journal of Formal Logic 47(3): 371–384.

da Costa Newton Carneiro Affonso. 1975. “Remarks on Ja´skowski’s discussive logic”. Reports on Mathematical Logic 4: 7–16.

da Costa Newton Carneiro Affonso, Lech Dubikajtis. 1977. “On Ja´skowski’s discussive logic”. In: Non-Classical Logics, Model Theory and Computability. Proceedings of the Third Latin-American Symposium on Mathematical Logic, Campinas, Brazil, July 11-17, 1976, ed. A. I. Arruda, N.C. A. da Costa, R. Chuaqui. Vol. 89 of Studies in Logic and the

Foundations of Mathematics Amsterdam, New York, Oxford: North-Holland Publishing Company. pp. 37–56.

Dunin-K˛eplicz Barbara, Alina Powała, Andrzej Szałas. 2018. “Variations on Ja´skowski’s Discursive Logic”. In: The Lvov-Warsaw School. Past and Present, ed. Ángel Garrido,

Urszula Wybraniec-Skardowska. Cham: Springer International Publishing. pp. 485–497. https://doi.org/10.1007/978-3-319-65430-0_34

Feys Robert. 1965. Modal Logics. Vol. 4 of Collection de Logique Mathematique, Série B Louvain and Paris: E. Nauwelaerts and Gauthier-Villars. Edited with some complements by Joseph Dopp.

Furmanowski Tomasz. 1975. “Remarks on discussive propositional calculus”. Studia Logica 34: 39–43. https://doi.org/10.1007/BF02314422

Jarmu˙zek Tomasz. 2021. “Relating semantics as fine-grained semantics for intensional logics”. In: Logic in High Definition, ed. A. Giordani, J. Malinowski. Trends in Logic, Vol. 56. Springer. pp. 13–30.

Ja´skowski Stanisław. 1948. “Rachunek zda´n dla systemów dedukcyjnych sprzecznych”. Studia Societatis Scientiarum Torunensis Sect. A, I(5): 57–77.

Ja´skowski Stanisław. 1949. “O koniunkcji dyskusyjnej w rachunku zda´n dla systemów dedukcyjnych sprzecznych”. Studia Societatis Scientiarum Torunensis Sect. A, I(8): 171-172.

Ja´skowski Stanisław. 1999a. “On the discussive conjunction in the propositional calculus for inconsistent deductive systems”. Logic and Logical Philosophy 7: 57–59. A new translation of the original Polish paper (Ja´skowski 1949).

Ja´skowski Stanisław. 1999b. “A propositional calculus for inconsistent deductive systems”.

Logic and Logical Philosophy 7: 35–56. A new translation of the original Polish paper

(Ja´skowski 1948).

Kotas Jerzy. 1974. “The axiomatization of S. Ja´skowski’s discussive system”. Studia Logica 33(2): 195–200. https://doi.org/10.1007/BF02120494

Kotas Jerzy. 1975. “Discussive sentential calculus of Ja´skowski”. Studia Logica 34(2): 149-168. https://doi.org/10.1007/BF02123384

Kotas Jerzy, Newton Carneiro Affonso da Costa. 1977. “On some modal logical systems defined in connexion with Ja´skowski’s problem”. In: Non-classical logics, model theory and computability. Proceedings of the Third Latin-American Symposium on Mathematical Logic, Campinas, Brazil, July 11–17, 1976, ed. A.I. Arruda, N.C.A da Costa, R. Chuaqui. Amsterdam, New York, Oxford: North-Holland Publishing Company. pp. 57–73.

Kovaˇc Sre´cko. 2008. “In what Sense is Kantian Principle of Contradiction Non-Classical?”. Logic and Logical Philosophy 17: 251–274. https://doi.org/10.12775/LLP.2008.013

Mruczek-Nasieniewska Krystyna, Marek Nasieniewski. 2005. “Syntactical and Semantical Characterization of a Class of Paraconsistent Logics”. Bulletin of the Section of Logic

34(4): 229–248.

Mruczek-Nasieniewska Krystyna, Marek Nasieniewski. 2019. “A Kotas-style characterisation of minimal discussive logic”. Axioms 8(4): 1–17. https://doi.org/10.3390/axioms8040108

Nasieniewski Marek, Andrzej Pietruszczak. 2008. “The Weakest Regular Modal Logic Defining Ja´skowski’s Logic D2”. Bulletin of the Section of Logic 37(3–4): 197–210.

Nasieniewski Marek, Andrzej Pietruszczak. 2011. “A method of generating modal logics defining Ja´skowski’s discussive logic 2”. Studia Logica 97(1): 161–182. https://doi.org/10.1007/s11225-010-9302-2

Nasieniewski Marek, Andrzej Pietruszczak. 2012. “On the weakest modal logics defining

Ja´skowski’s logic D2 and the 2-consequence”. Bulletin of the Section of Logic 41(3

4): 215–232.

Nasieniewski Marek, Andrzej Pietruszczak. 2013. “On Modal Logics Defining Ja´skowski’s D2-Consequence”. In: Paraconsistency: logic and applications, ed. Koji Tanaka,

Francesco Berto, Edwin Mares, Francesco Paoli. Vol. 26 of Logic, Epistemology and the

Unity of Science. Dordrecht: Springer International Publishing AG Switzerland. pp. 141

161. https://doi.org/10.1007/978-94-007-4438-7_9

Nasieniewski Marek, Andrzej Pietruszczak. 2014a. “Axiomatisations of minimal modal logics defining Ja´skowski-like discussive logics”. In: Trends in Logic XIII: Gentzen’s and Ja´skowski’s heritage 80 years of natural deduction and sequent calculi, ed. Andrzej Indrzejczak, Janusz Kaczmarek, Michał Zawidzki. Łód´z: Wydawnictwo Uniwersytetu Łódzkiego. pp. 149–163.

Nasieniewski Marek, Andrzej Pietruszczak. 2014b. “On modal logics defining a Ja´skowski

like discussive logic”. In: Handbook of the 5th World Congress on Paraconsistency, February 13-17, 2014, Kolkata, India, ed. Arthur Buchsbaum Jean-Yves Beziau, Alvaro Altair. Indian Statistical Institute. pp. 67–68.

Nicolás-Francisco Ricardo Arturo. 2022. “On Polish-‘via modalisation’ approach to paraconsistency”. Edukacja Filozoficzna 74: 161–182.

Orayen Raúl. 1989. Lógica, significado y ontología. México: UNAM.

Perzanowski Jerzy. 1975. “On M-fragments and L-fragments of normal modal propositional logics”. Reports on Mathematical Logic 5: 63–72.

Rodrigues Abilio, Marek Nasieniewski, Ricardo Arturo Nicolás-Francisco. 2025. “Someremarks on two seminal approaches to paraconsistency: Stanisław Ja´skowski and Newton da Costa”. Studia Logica 13: 1139–1194.

Thomas Ivo. 1964. “Modal Systems in the Neighbourhood of T”. Notre Dame Journal of Formal Logic 5(1): 59–61. https://doi.org/10.1305/ndjfl/1093957739

Urchs Max. 1995. “Discursive logic towards a logic of rational discourse”. Studia Logica 54: 231–249. https://doi.org/10.1007/BF01063153

Von Wright Georg Henrik. 1951. “I. Deontic Logic”. Mind 60(237): 1–15. https://doi.org/

10.1093/mind/LX.237.1

Studies in the History of Philosophy

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Published

2025-12-19

How to Cite

1.
NASIENIEWSKI, Marek and NICOLAS FRANCISCO, Ricardo Arturo. On some concepts constituting discussive logic. Studies in the History of Philosophy. Online. 19 December 2025. Vol. 16, no. 4, pp. 19-34. [Accessed 23 February 2026]. DOI 10.12775/szhf.2025.030.
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